dear advice givers

So, givers of advice, a question.

I'm applying for jobs but have no references. Well, I do have one, my teacher from school, but otherwise my supervisors from previous jobs aren't even allowed to be references. Both places forbid potential employers to talk to specific supervisors, only to someone in the HR departments. And co-workers apparently don't count as references, and my local friends are really more acquaintances who I wouldn't bother with a request like this.

So. What do I do? Just give one reference, or give supervisors as references with a note saying they can't actually talk to said supervisors?

I am actually kind of stunned that these applications want the names of HR people, supervisors, AND references from each job. Probably a credit check, too. It's crazy.